The specific rotation of a chemical compound [α] is defined as the observed angle of optical rotation α when plane-polarized light is passed through a sample with a path length of 1 decimeter and a sample concentration of 1 gram per 1 millilitre. The specific rotation of a pure material is an intrinsic property of that material at a given wavelength and temperature. Values should always be accompanied by the temperature at which the measurement was performed and the solvent in which the material was dissolved. Often the temperature is not specified; in these cases it is assumed to be room temperature. The formal unit for specific rotation values is deg cm² g^-1 but scientific literature uses just degrees. A negative value means levorotatory rotation and a positive value means dextrorotatory rotation. Some examples: A chemical compound is a chemical substance consisting of two or more different chemically bonded chemical elements, with a fixed ratio determining the composition. ... When polarized light is passed through a substance containing chiral molecules (or nonchiral molecules arranged asymmetrically), the direction of polarization can be changed. ... A decimetre is a measurement of length, measuring 10 centimetres or one-tenth of a metre millimetre << centimetre << decimetre << metre << kilometre ... BIC pen cap, about 1 gram. ... The millilitre is the equivalent of a cubic centimetre. ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1／360 of a full rotation. ... Levorotation (also spelled laevorotation) is the counterclockwise rotation of plane polarized light. ... Dextrorotation is the property of rotating plane polarized light to the right. ...

• Sucrose +66.47°
• cholesterol −31.5°
• Camphor +44.26°
• Penicillin V +223°
• taxol −49°
• (S)-bromobutane +23.1°
• (R)-bromobutane −23.1°
• (+)-cavicularin +168.2°

Optical rotation is measured with an instrument called a polarimeter. There is a linear relationship between the observed rotation and the concentration of optically active compound in the sample. There is a non-linear relationship between the observed rotation and the wavelength of light used. Specific rotation is calculated using either of two equations, depending on the sample you are measuring: Sucrose (common name: table sugar, also called saccharose) is a disaccharide (glucose + fructose) with the molecular formula C12H22O11. ... Cholesterol is a sterol (a combination steroid and alcohol) and a lipid found in the cell membranes of all body tissues, and transported in the blood plasma of all animals. ... R-phrases 11-20/21/22-36/37/38 S-phrases 16-26-36 RTECS number EX1260000 (R) EX1250000 (S) Supplementary data page Structure and properties n, εr, etc. ... Penicillin nucleus Penicillin (sometimes abbreviated PCN) refers to a group of β-lactam antibiotics used in the treatment of bacterial infections caused by susceptible, usually Gram-positive, organisms. ... Paclitaxel is a drug used in the treatment of cancer. ... Cavicularin is a phenolic secondary metabolite isolated from the liverwort Cavicularia densa. ... A polarimeter is a scientific instrument for measuring the rotation of the plane of polarized light as it passes through a sample of a compound which exhibits optical activity. ... When polarized light is passed through a substance containing chiral molecules (or nonchiral molecules arranged asymmetrically), the direction of polarization can be changed. ...

For pure liquids:

In this equation, l is the path length in decimeters, and d is the density of the liquid in g/mL, for a sample at a temperature T (given in degrees Celsius) and wavelength λ (in nanometers). If the wavelength of the light used is 589 nanometer (the sodium D line), the symbol “D” is used. The sign of the rotation (+ or -) is always given. A nanometre (American spelling: nanometer) is 1. ...

°

For solutions, a different equation is used:

In this equation, l is the path length in decimeters and c is the concentration in g/100mL, for a sample at a temperature T (given in degrees Celsius) and wavelength λ (in nanometers). If the wavelength of the light used is 589 nanometer (the sodium D line), the symbol “D” is used. The sign of the rotation (+ or -) is always given. When using this equation, the concentration and the solvent are always provided in parentheses after the rotation. The rotation is reported using degrees, and no units of concentration are given (it is assumed to be g/100mL). A nanometre (American spelling: nanometer) is 1. ...

For example:

° (c 1.0, EtOH)

This solution equation is incorrectly represented in many textbooks and on many websites as:

(concentration in g/mL)

Mathematically, the two forms are the same, but chemically they are very different. Using the incorrect form of the equation will produce problems because the concentration will have the incorrect units. Because the units are not reported, this can produce difficulties for those trying to use the data later.

If a compound has a very large specific rotation or a sample is very concentrated, the actual rotation of the sample may be larger than 180°, and so a single polarimeter measurement cannot detect when this has happened (for example, the values +270° and –90° are not distinguishable, nor are the values 361° and 1°). In these cases, measuring the rotation at several different concentrations allows one to determine the true value.

In cases of very small or very large angles, one can also use the variation of specific rotation with wavelength to facilitate measurement. Switching wavelength is particularly useful when the angle is small. Many polarimeters are equipped with a mercury lamp (in addition to the sodium lamp) for this purpose.

The variation of specific rotation with wavelength is the basis of optical rotary dispersion (ORD) that can be used to elucidate the absolute configuration of certain compounds.

Measuring optical rotation provides a way to assess optical purity of a sample containing a mixture of enantiomers. For example, if a sample of bromobutane measured under standard conditions has an observed rotation of −9.2°, this indicates that the net effect is due to (100%)(9.2°/23.1°)=40% of the R enantiomer. The remainder of the sample is a racemic mixture of the enantiomers (30% R and 30% S), which has no net contribution to the observed rotation. The enantiomeric excess is 40%; the total concentration of R is 70%. In chemistry, enantiomers are stereoisomers that are mirror images of each other. ... In chemistry, a racemate is a mixture of equal amounts of left- and right-handed stereoisomers of a chiral molecule. ... In chemistry two stereoisomers are said to be enantiomers if one can be superimposed on the mirror image of the other. ...